Why does the entire mesh move in this model?
The problem is that you have turned on Proportional Editing in the Edit Mode. You might have either pressed O or selected the icon shown in the image by accident:

You can switch it off by pressing O again or just click the icon to disable Proportional Editing.
Notice the circle that appears when you move, scale or rotate the object controls how much of the mesh should move with the select edge, vertex or face so
it doesn't move the entire mesh with it.
To put it simply, usually the tool is used to get uniform curved surfaces. You can further control the tool by clicking on the drop-down menu nearby the icon. You can control the diameter of the circle by scrolling the middle mouse button up or down. That is used to control the amount of vertices affected by it. In other words: All vertices inside the circle will be effected by the function.